The numbers can be arranged as follows
(1 - 1) + 2 - (3 + 4) + (5 + 6 + 7 + 8 + 9) = 30 How to solve the math questionThe math question is solved using the idea of PEMDAS which is an acronym for order of arrangement of mathematical operations as
the full meaning include
P - parenthesis
E - exponents
M - multiplication
D - division
A - addition
S - subtraction
Applying the sequence the to make the expression 1 2 3 4 5 6 7 8 9 equal to 30 using addition and subtraction signs:
(1 - 1) + 2 - (3 + 4) + (5 + 6 + 7 + 8 + 9) = 30
You can use parentheses to group the numbers and then add or subtract the groups to get the desired result.
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12. Find (a) the perimeter and (b) the area of the
figure. Dimensions are in meters.
8
8
The perimeter of the given figure is: 36 +16√5 ft ≈ 71.777 ft
The area of the figure is: 288 ft²
How to find the area of a region?Supposing that there is no direct formula available for deriving the area, we can derive the area of that region by dividing it into smaller pieces, whose area can be known directly. Then summing all those pieces' area gives us the area of the main big region.
We know that the perimeter is the total length of all the sides. The length of the horizontal sides is; 8 ft + 10 ft = 18 ft.
The length of the slant sides can be found by the Pythagorean theorem.
For side length s, we have;
s^2 = 8^2 + 16^2
s^2 = 64 +256 = 320
s = √320 = 8√5
Then the perimeter;
P = 2(8√5 + 18) = 36 +16√5 ≈ 71.777 . . . feet
Area, A = bh
where b is the base and h is the height.
A = (18 ft)(16 ft) = 288 ft²
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A cylinder shaped dispenser holds 5,652 cubic centimeters of liquid soap and is now full. The radius of the dispenser is 7. 5 centimeters. What is the difference between the height of the soap in the full dispenser and the height when 4,239 cubic centimeters of soap remains in the dispenser? use 3. 14 for pi. Enter your answer in the box.
Answer:
The difference in height is 8cm
Step-by-step explanation:
Volume of a cylinder=hπr²
When the bottle is full 5652:
5652=hπr²
5652=h*3.14*7.5²
5652=h*176.625
5652/176.625=h
Height=32cm
When the bottle is full by 4239:
4239=hπr²
4239=h*3.14*7.5²
4239=h*176.625
4239/176.625=h
Height=24cm
Difference in height:
32-24=8
The difference in height is 8cm
A spotlight is fixed on the ground 35m from the town hall. It is switched on at night to illuminate the building. When Dirk stands 5m in front of the light, his shadow is as tall as the building, If Dirk is 1.40m tall, how tall is the town hall?
To answer this question, we need to use some basic trigonometry. We know that Dirk's shadow is as tall as the town hall and that Dirk is 1.40m tall. So, if we can determine the angle of elevation of the spotlight, we can calculate the height of the town hall.
Let's call the angle of elevation "α" and the distance from the spotlight to the town hall "d". To determine α, we can use the tangent function.
tan α = opposite/adjacent = (d-5)/35 = (30/35) = 0.8571
The angle of elevation is arctan(0.8571) = 53.13°.
Now, we can use the sine function to calculate the height of the town hall:
sin α = opposite/hypotenuse = 1.4/d
d = 1.4/sin 53.13° = 16.2m
Therefore, the town hall is 16.2m tall.
Given: log a 2 = 4, log a 3 = 5, log a 5 = 8. Find log a 60.
A. 2.9
B. 1.46
C. .32
D. 2.1
The solution of the logarithm expression logₐ 60 is 2.1. Therefore, the answer is D.
How to solve logarithm?The logarithm expression can be solved as follows; Using the logarithm rule,
Law of multiplication of logarithm,
logₐ x + logₐ y = logₐ xy
Therefore,
logₐ 2 = 4
logₐ 3 = 5
logₐ 5 = 8
Hence, let's find logₐ 60.
logₐ 5 + logₐ 3 + logₐ 2 + logₐ 2 = logₐ (5 × 3 × 2 × 2) = logₐ 60
Hence,
0.8 + 0.5 + 0.4 + 0.4 = 2.1
Therefore,
logₐ 60 = 2.1
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The value of log a 60 is 21. The correct option is D.
What is a Logarithm?Logarithms are another way of writing exponents.
Logarithm is nothing but another way of expressing exponents and can be used to solve problems that cannot be solved using the concept of exponents only.
log a 60 = log a (12 x 5)
log a 60 = log a 12 x log a 5
log a 60 = log a (4 x 3) x log a 5
log a 60 = log a 4 x log a 3 x log a 5
log a 60 = 2 log a 2 x log a 3 x log a 5
Substituting the values for the logs
log a 60 = 2 (4) + 5 + 8
log a 60 = 21
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3. Juanita put $2,000 in a 6-month CD. The interest rate is 3%. The interest is compounded quarterly. What is the interest for the first quarter? What will be the value of the CD when it matures?
The interest for the first quarter would be $ 15
The value of the CD when it matures is $ 2, 030. 11
How to find the value of the CD ?The interest is said to compound quarterly which means that the periodic interest rate per quarter is:
= 3 % / 4
= 0. 75 % per quarter
The interest in the first quarter :
= 0. 75 % x 2, 000
= $ 15
The value of the CD at maturity is:
= 2, 000 x ( 1 + 0. 75% ) ²
= $ 2, 030. 11
Note : 2 periods because 6 months is 2 quarters.
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A helicopter hovers 1025 feet above a small island.The figure shows that the ang;e of depression from the helicopter to point P is 32 degrees. How far off the coast, to the nearest foot, is the island?
Answer:
The island is 728 feet off the coast.
Step-by-step explanation:
Teresa needs to make a total of 95 deliveries this week. So far she has completed 76 of them. What percentage of her total deliveries has Teresa completed?
Answer:
Step-by-step explanation:
its Reduced to 2 / 5, which is 40 percent. Maria has 40 percent of her work completed
A) In a geometric sequence, t_(1)=625 and the common ratio is r=(1)/(5). For what value of n is t_(n)=(1)/(25)?
b) Determine whether each sequence is arithmetic, geometric, or neither. Then find a formula for the n-th term of the sequence.
(2)/(5),(3)/(6),(4)/(7),(5)/(8),dots
Answer:
Step-by-step explanation:
A) In a geometric sequence, t_(1)=625 and the common ratio is r=(1)/(5). For what value of n is t_(n)=(1)/(25)?
Step 1: Write the formula for the nth term
The formula for the nth term of a geometric sequence is t_n = t_1 * r^(n-1), where t_1 is the first term and r is the common ratio.
Step 2: Substitute the given values into the formula
t_n = 625 * (1/5)^(n-1)
Step 3: Solve for n when t_n = (1/25)
(1/25) = 625 * (1/5)^(n-1)
(1/25) / 625 = (1/5)^(n-1)
(1/5)^(n-1) = (1/25) / 625
(n-1) = log base (1/5) of ((1/25) / 625)
Step 4: Solve for n
n = 1 + log base (1/5) of ((1/25) / 625)
The value of n is the number of terms that have passed when t_n = (1/25).
B) (2)/(5),(3)/(6),(4)/(7),(5)/(8),...
Step 1: Determine the type of sequence
A sequence is an arithmetic sequence if the difference between any two consecutive terms is constant. Since this sequence does not have a constant difference, it is not an arithmetic sequence.
A sequence is a geometric sequence if the ratio between any two consecutive terms is constant. We can see that the ratio between any two consecutive terms is constant, so this sequence is a geometric sequence.
Step 2: Find the common ratio
To find the common ratio, we can divide any two consecutive terms. For example, the common ratio is (3/6) / (2/5) = (3/2) / (6/5) = 5/6.
Step 3: Write the formula for the nth term
The formula for the nth term of a geometric sequence is t_n = t_1 * r^(n-1), where t_1 is the first term and r is the common ratio.
Step 4: Substitute the given values into the formula
To use this formula, we need to know the value of t_1. We are given t_1 = (2/5), so:
t_n = (2/5) * (5/6)^(n-1)
This is the formula for the nth term of the sequence (2)/(5),(3)/(6),(4)/(7),(5)/(8),...
An older person is 5 years older than four times the age of a younger person.
The sum of their ages is 30. Find their ages.
Their ages are _____
(Use a comma to separate answers as needed.)
Their ages are 5 years, 25 years
How to find their ages?Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.
Let L and Y represent the age of the older person and younger person respectively.
Using the given information, we can write:
L = 4Y + 5 --- (1)
L + Y = 30 --- (2)
From (2):
L = 30 - Y --- (3)
Put (3) in (1):
L = 4Y + 5
30 - Y = 4Y + 5
4Y + Y = 30 - 5
5Y = 25
Y = 25/5
Y = 5 years
Put Y = 5 into (3):
L = 30 - Y
L = 30 - 5
L = 25 years
Their ages are 5 years, 25 years
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Put the equation y=x^2-8x+12 into the form y= (x-h)^2+k
Answer:
y = ( x - 4 )² - 4
Step-by-step explanation:
a² ± 2ab + b² = ( a ± b )²
~~~~~~~~~~~~
y = x² - 8x + 12
y = ( x² - 2(4)(x) + 4² ) - 4² + 12 = ( x - 4 )² - 4
y = ( x - 4 )² - 4
7. Jane was shopping for oranges, which were listed $0.75 each. She brought seven the discount, she was charged $4.30 before tax. What was the percent discount on each oranges to the checkout lane, where she learned that there was a sale on oranges. With orange?
The discount on each orange is 81.3%
What is discount?The discount equals the difference between the price paid for and it's par value. Discount is a kind of reduction or deduction in the cost price of a product.
A sales discount is a reduced price offered by a business on a product or service.
The total price for the oranges is;
0.75 × 7 = $5.25
She paid $ 4.30 for the oranges, this means that the discount = 5.25-4.30 = $0.95
Therefore the percentage discount on all the oranges = 0.95/5.25 × 100
= 18.1%
by discount each orange = 4.30/7 =$ 0.61
Therefore the discount on each orange = 0.61/0.75 ×100 = 81.3 %
Therefore the discount on each orange is 81.3%
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Learning Page
QUESTION
We'd like to simulate the probabilities involved when Ivanna shoots two penalty kicks.
The table below gives a simulation of Ivanna shooting penalty kicks.
The table shows 10 trials. Each trial has two simulated penalty kicks.
Each simulated penalty kick is a random number from 1 to 100.
Trial
1
2
3
4
5
6
7
8
an
First
penalty kick
91
10
33
88
92
56
More Practice
4
92
45
40
39
Second
penalty kick
43
82
29
58
86
45
11
36
6
43
The correct answers are given below:
(a) 1 to 55
(b) 40%
How to solve thisSince Mansour scores 55% of his kicks, we'd want exactly 55% of the simulated numbers to denote Mansour scoring a penalty, thus, 1 to 5 is a possible range.
To find the percentage of trials where Mansour scored exactly one penalty, we have to count the trials where one of the simulated numbers is in the range of 1 to 5 (denoting Mansour scoring the penalty) and the other is in the range of 56 to 100 (denoting Mansour missing the penalty)
Trails 1, 3, and 4, 6 are such trials. Thus, Mansour scored exactly one penalty kick in 40% of the trials.
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pls help with this
Find the length of side x in simplest radical form with a rational denominator.
The length of x is 6 in the given triangle.
What is Trigonometry?The branch of Mathematics which studies relationships between side lengths and angles of triangles.
We have to find the value of x in the given triangle.
We know that tan theta is the ratio of opposite side by adjacent side.
The opposite side is x and the adjacent side has √12
tan60=x/√12
√3=x/√12
x=√12√3
x=√36
x=6
Hence, the length of x is 6.
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Samir made a scale drawing of a city. He used the scale 5 inches = 1 yard. What scale factor
does the drawing use?
Simplify your answer and write it as a fraction.
Answer:
the scale factor that Samir used in his drawing is 5/1.
Step-by-step explanation:
Here's a step by step explanation of how to find the scale factor of a drawing:
Identify the scale used in the drawing. In this case, the scale used in Samir's drawing is 5 inches = 1 yard.
Express the scale as a ratio between the two sizes. In this case, the ratio is 5 inches : 1 yard.
Simplify the ratio, if possible. In this case, the ratio 5 inches : 1 yard can be simplified to 5/1.
The simplified ratio, 5/1, is the scale factor of the drawing. This means that for every 5 inches on the drawing, the actual length in the real world is 1 yard.
So, the scale factor that Samir used in his drawing is 5/1.
Explain in words the graphical transformations that f(x) undergoes to become
f(x + 9) − 1.
The transformations taking place in the given function is a horizontal left ward shift of 9 units and 1 unit upward vertical shift.
What is transformation?A Transformation in Math is a process of moving an object (two-dimensional shape) from its original position to a new position.
Given that, a function f(x) undergo some transformations to become f(x+9)-1,
We know that,
Vertical Shifting:
Adding a constant to a function will shift its graph vertically (i.e. y = f (x) + c). Adding a positive constant c will shift the graph upward c units, while adding a negative constant c will shift it downward c units.
Horizontal Shifting:
Horizontal shifts are inside changes that affect the input (x-) axis values and shift the function left or right. Combining the two types of shifts will cause the graph of a function to shift up or down and right or left.
Therefore, there is transformation of a horizontal and vertical shift.
Hence, the transformations taking place in the given function is a horizontal left ward shift of 9 units and 1 unit upward vertical shift.
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Guess the value of the following limit (if it exists) by evaluating the function at the given numbers.
The value of the limit of the rational function evaluated x = - 5 is equal to - 6.
How to determine the exact value of a limit at a given value
In this problem we find the limit of rational function evaluated at a given value. According to the statement, there is apparently a discontinuity at x = 5. The expression can be simplified by algebra properties:
[tex]\lim_{x \to - 5} \frac{x^{2} + 4 \cdot x - 5}{x + 5}[/tex]
[tex]\lim_{x \to -5} \frac{(x + 5)\cdot (x - 1)}{(x + 5)}[/tex]
[tex]\lim_{x \to - 5} (x - 1)[/tex]
Then, we can complete the table by means of the following expression:
f(x) = x - 1
x = - 5.01
f(- 5.01) = - 5.01 - 1
f(- 5.01) = - 6.01
x = - 5.001
f(- 5.001) = - 5.001 - 1
f(- 5.001) = - 6.001
x = - 5.0001
f(- 5.0001) = - 5.0001 - 1
f(- 5.0001) = - 6.0001
x = - 5
f(- 5) = - 5 - 1
f(- 5) = - 6
x = - 4.9999
f(- 4.9999) = - 4.9999 - 1
f(- 4.9999) = - 5.9999
x = - 4.999
f(- 4.999) = - 4.999 - 1
f(- 4.999) = - 5.999
x = - 4.99
f(- 4.99) = - 4.99 - 1
f(- 4.99) = - 5.99
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A crew of construction workers are disassembling the inside of a building and dropping things into dumpsters at the base of the building. The equation Va=(64d)122
is used to find the average velocity, or speed, in feet per second of an object that has fallen a distance of d feet. What is the average velocity, to the nearest hundredth, of a ceiling tile that fell 43 feet ?
The average velocity, to the nearest hundredth, of a ceiling tile that fell 43 feet is 344 feet per second
What is speed?Velocity is the pace and direction of an item's movement, whereas speed is the time rate at which an object is travelling along a route.
Given that the formula for the speed of a falling object is v= √64d,
where v is the speed of the object in feet per second and d is the distance the object has fallen, in feet.
And also given that d = 43 feet.
Substituting the value to the formula,
v = √64 (43)
v = 8 x 43
v = 344
Therefore, 344 feet per second is the velocity.
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find the sum of 10+3x,25-4x+2x^,3x^-5x and -x^+2x+15
Answer:
50 + 5x^2 + 4x.
Step-by-step explanation:
To find the sum of the expressions, we need to simplify each expression first and then add them up.
10 + 3x represents the first expression.
25 - 4x + 2x^2 represents the second expression. By simplifying this expression, we get 25 + 2x^2 - 4x.
3x^2 - 5x represents the third expression.
-x^2 + 2x + 15 represents the fourth expression.
Adding all four expressions gives us:
10 + 3x + 25 + 2x^2 - 4x + 3x^2 - 5x - x^2 + 2x + 15
By combining like terms, we get:
10 + 5x^2 + 4x + 25 + 15
The final simplified sum is:
50 + 5x^2 + 4x.
Biketown is a 100-year-old manufacturer of bicycles. It has a loyal customer base who appreciate the workmanship of its bicycles and are willing to pay more for its products. In order to compete with lower priced manufacturers, biketown has purchased a new automated machine to assemble bicycles that is more efficient and less costly than the existing manual assembly process. Select who would not be a stakeholder in this business decision.
Someone who is not a stakeholder in this business does not have any interest or concern in Biketown's decision to purchase a new automated machine.
In this scenario, stakeholders for Biketown's decision to purchase are Customers who appreciate the workmanship of Biketown's bicycles, Employees who are involved in the assembly process, Shareholders who have invested in the company, Suppliers who provide materials or components for the bicycles.
Local community members who may be impacted by the company's operations or decisions. An individual who has no knowledge of or interaction with Biketown or the bicycle industry, and therefore has no stake in the decision.
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Stats Determine the y-intercept and slope from the equation: y = 5.8 +2.5x
The slope is 2.5
The y-intercept is 5.8.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
y = 5.8 + 2.5x
This is in the form of y = mx + c
So,
m = 2.5
And,
The y-intercept is when x = 0.
So,
y = 5.8 + 2.5x
Substitute x = 0,
y = 5.8
Thus,
Slope is 2.5
The y-intercept is 5.8.
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help me please dont know what im doing
The amount of natural oil needed to make 869 liters of Petrolyn oil is given as follows:
1520.75 liters.
How to obtain the amount of natural oil?The necessary amount of natural oil is obtained applying the proportions in the context of this problem.
Considering the ratio given in the problem, a rule of three is established, as follows:
7 liters of natural oil - 4 liters of Petrolyn oil.
n liters of natural oil - 869 liters of Petrolyn oil.
Applying cross multiplication, the desired amount is obtained as follows:
4n = 7 x 869
n = 7 x 869/4
n = 1520.75 liters.
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Question content area top
Part 1
Find the measure of side a.
Side a will be 58cm.In mathematics, a side is a feature of a geometric shape.
A side: What is it?The "A-side" of a record, which is the main song, is issued as a single. The "A-side" of an album is the side that this track is on. The word "side" is most frequently employed as a noun, however it can also be used as an adverb or a verb. The shapes we observe are made of points and lines (line segments) (vertices).
Finding the side, we obtain:
Given ∠A= 30°, b =100 cm .
In ΔABC,
tan A = [tex]\frac{a}{100}[/tex],
tan 30°= [tex]\frac{a}{100}[/tex]
0.577×100=a
a=57.7≅58 cm.
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A rectangular field is four times as long as it is wide. If the perimeter of the field is 400 yards, what are the field’s dimensions?
Answer:
Answer is in the attached photo.
Step-by-step explanation:
SolutionThe solution is in the attached photo, do take note the perimeter of the rectangle is:
2 x Length + 2 x Width.
Answer:
2 x Length + 2 x Width.
Step-by-step explanation:
Courtney can run a 1/4 mile in 2 minutes. At this rate, how many minutes will it take Courtney to
run 1.25 miles?
Answer:
10 minutes
Step-by-step explanation:
1/4 in 2 minutes
1 1/4 = 1/4 x 5
2 x 5 = 10
(That's REALLY good honestly)
If Z₁=3-2i
Z2=-2+3i
Z3=4+2i
Evaluate Z₂ Z3/Z₁
Answer:
32/13
Step-by-step explanation:
To evaluate the expression Z₂ * Z3 / Z₁, we first need to find the complex numbers Z₂ * Z3 and Z₁.
Z₂ * Z3 = -2 + 3i * 4 + 2i = (-8 + 14i) + (-6 + 6i) = -8 + 8i
Z₁ = 3 - 2i
So, Z₂ * Z3 / Z₁ = (-8 + 8i) / (3 - 2i)
We can simplify this expression by multiplying the numerator and denominator by the complex conjugate of the denominator, which is (3 + 2i).
Z₂ * Z3 / Z₁ = (-8 + 8i) / (3 - 2i) * (3 + 2i) / (3 + 2i) = (-8 + 8i) * (3 + 2i) / (3 - 2i) * (3 + 2i)
Z₂ * Z3 / Z₁ = ((-8 * 3 + 8 * 2i) + (8 * 3 + 8 * 2i)) / (3^2 + (-2i)^2) = (16 + 16i) / 13
Therefore, Z₂ * Z3 / Z₁ = (16 + 16i) / 13.
Isabel wants to pour 90.45 grams of salt into a container. So far, she has poured 55.2 grams. How much more salt should Isabel pour?
By subtraction we get that, Isabel has to pour 35.25 grams of salt into the container.
What is subtraction?The operation or process of finding the difference between two numbers or quantities is known as subtraction. To subtract a number from another number is also referred to as 'taking away one number from another'.
According to the information in question:
Total salt = 90.45 grams
Amount of salt poured = 55.2 grams
Thus, the total amount of salt left with her which has to be poured will be calculated by subtraction:
Amount of salt left = 90.45 - 55.2
= 35.25 grams
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Rewrite in simplest terms:-2(-10v+1)-6v
Answer:
14v-2
Step-by-step explanation:
1. distribute
2. combine like terms
see photo for more information
2.2 Kiri's older brother asked the 25 students in his class. 11 students said they think aliens exist. Which class has a greater percentage of students who think aliens exist: Kiri's or her brother's? Explain your thinking.
Answer:
The percentage of students in Kiri's brother's class who think aliens exist is 11/25 = 44%.
Since the number of students in Kiri's class is not given, it's not possible to compare the percentage of students in Kiri's class who think aliens exist to the percentage in her brother's class. We need to know the number of students in Kiri's class and the number of students who believe in aliens in order to compare the percentages.
A researcher tested two groups (females and males) of rats on memory performance. The following scores are for the number of correct choices they made on the task:
The probability distribution does not add up to 1.0, in other words.
What is meant by probability?Probability, in its simplest form, gauges the likelihood that something will happen. When we are unsure of how an event will turn out, we might talk about the likelihood of different outcomes.The study of events susceptible to probability is known as statistics. The probability is frequently stated as a ratio between the total number of outcomes in the sample space and the number of positive outcomes.This is how it is written: Number of Favorable Outcomes P(E) = Probability of an Event (Sample space).Probability can be divided into four main categories: axiomatic, axiomatic, classical, and empirical. The area of mathematics known as probability studies the likelihood that a random event will occur.The complete question is:
A researcher records the number of mistakes made during a memory skills task. He finds that the probability that participants in this study made 0 mistakes is p = .22; made 1 mistake is p = .30; made 2 mistakes is p = .16; made 3 mistakes is p = .12; and made 4 or more mistakes is p = .25. Is this probability distribution accurate?
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Answer:
It is not accurate
Step-by-step explanation:
If the complete question is:
A researcher records the number of mistakes made during a memory skills task. He finds that the probability that participants in this study made 0 mistakes is p = .22; made 1 mistake is p = .30; made 2 mistakes is p = .16; made 3 mistakes is p = .12; and made 4 or more mistakes is p = .25. Is this probability distribution accurate?
THEN:
To determine whether the probability distribution is accurate, we need to check two conditions:
The sum of the probabilities should be equal to 1.
All probabilities should be between 0 and 1.
Let's check these conditions:
Sum of probabilities:
p(0) + p(1) + p(2) + p(3) + p(4 or more) = 0.22 + 0.30 + 0.16 + 0.12 + 0.25 = 1.05
The sum of the probabilities is greater than 1, which violates the first condition. Therefore, this is not a valid probability distribution.
All probabilities should be between 0 and 1:
The probability of making 0, 1, 2, or 3 mistakes are all between 0 and 1, so they satisfy this condition.
However, the probability of making 4 or more mistakes is 0.25, which is a valid probability, but it implies that the probability of making 0, 1, 2, or 3 mistakes is negative, which is impossible. Therefore, this distribution does not satisfy this condition.
Since this probability distribution violates both conditions for a valid probability distribution, it is not accurate, and the researcher should revise their data.
Each worker at a store gets paid $15.90 for that first 40 hours worked. After 40 hours, they earn time and a half wages. Every employee has a 28% of his/her gross pay deducted for taxes, insurance etc. how much of a net pay does each worker take home?
Each worker would take home a net pay of $586.71.
What is the net pay?
The net pay is the amount of money that an employee takes home after all deductions have been made from their gross pay. Gross pay is the total amount of money an employee earns before taxes and other deductions are taken out.
To calculate net pay, you need to subtract all the required deductions from the employee's gross pay.
To calculate the net pay for each worker, we first need to determine their gross pay. The gross pay will depend on the number of hours they worked and whether they worked any overtime.
For the first 40 hours worked, each worker earns $15.90 per hour, so their gross pay for those hours would be:
Gross Pay for 40 hours = $15.90/hour x 40 hours = $636
For any hours worked beyond 40, the worker earns time and a half wages. This means they earn 1.5 times their regular hourly wage of $15.90, or $23.85 per hour. So, if they worked, for example, 45 hours in total, the additional 5 hours would be paid at the overtime rate, resulting in an additional gross pay of:
Gross Pay for 5 overtime hours = $23.85/hour x 1.5 x 5 hours = $178.88
Therefore, their total gross pay would be:
Total Gross Pay = Gross Pay for 40 hours + Gross Pay for 5 overtime hours = $636 + $178.88 = $814.88
Now, we need to calculate the deductions, which we are told are 28% of the gross pay. So the total deductions would be:
Total Deductions = 28% x $814.88 = $228.17
Finally, to determine the net pay, we need to subtract the total deductions from the gross pay:
Net Pay = Gross Pay - Total Deductions = $814.88 - $228.17 = $586.71
Therefore, each worker would take home a net pay of $586.71.
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